A body can have zero average velocity but not zero average speed. Justify.
Question
A body can have zero average velocity but not zero average speed. Justify.
Solution
Sure, here is the justification:
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Velocity is a vector quantity, which means it has both magnitude (speed) and direction. Average velocity is calculated by total displacement (change in position) divided by total time taken. Displacement takes into account the direction of motion.
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If a body returns to its starting point after moving around for some time, its total displacement is zero. Therefore, its average velocity, being displacement divided by time, is also zero.
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However, speed is a scalar quantity, which only considers the magnitude of motion, not the direction. Average speed is calculated by total distance covered divided by total time taken. Distance is always a positive quantity, it only considers how much ground has been covered.
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Even if a body returns to its starting point, the path it travelled still contributes to the total distance. Therefore, unless the body did not move at all, the average speed cannot be zero.
In conclusion, a body can have zero average velocity if it returns to its starting point, but it cannot have zero average speed unless it did not move at all.
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